Title

Author

Date of Award

12-2007

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. M. Niewiadomska Bugaj

Second Advisor

Dr. Joshua Naranjo

Third Advisor

Dr. J. C. Wang

Fourth Advisor

Dr. Daniel Frobish

Abstract

We consider two-part models that are mixtures of a point-mass variable with all mass at zero and a continuous random variable. The model may assume a particular distributionh(x) for the continuous part such as a log-normal or a gamma. The response variable is defined as y=(x, d), where d=1 if x > 0 and d=0 if x = 0. The probability distribution function has the following form: fx,d=p 1-d×1-p ×hx d.

Lachenbruch (1976, 2001) proposed several tests to compare means of two populations for this type of data. We proposed a two-part Wald test and a two-part likelihood ratio test to compare &thetas; = (p, m) (p is the proportion of zeros and m is the mean of h(x)), hence the equality of overall means in K independent populations where h( x) is a lognormal distribution. These two test statistics have asymptotically chi-square distribution with 2(k − 1) degrees of freedom. A simulation study was conducted to compare the size and the power of the proposed tests with several other tests (ANOVA, Welch, Brown-Forsythe, and Kruskal-Wallis).